Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 4, −2, 1, …

a₁ = 4r = −0.5n = 9
S9 =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 12·(−2/5)ᵏ.

a = 12r = −2/5k₀ = 1
S =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ k·2ᵏ/3ᵏ. Find L = lim |ak+1/ak|.

ak = k·2ᵏ/3ᵏ
L =
5.Hard

f(x) = sin x is approximated at x = 1 by its Maclaurin polynomial of degree n. With the Lagrange bound M·|x|ⁿ⁺¹/(n + 1)! and M = 1, find the smallest degree n that guarantees an error below 1 × 10⁻⁶.

f(x) = sin xx = 1M = 1ε = 1 × 10⁻⁶
n =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =

Answer key

  1. 1. S9 = 2.672
  2. 2. S = −3.429
  3. 3. L = 1.104
  4. 4. L = 0.6667
  5. 5. n = 9
  6. 6. S = 0.4444

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